Question

In a factory, 2000 kg of metal needs to be lifted by an engine through a distance of 12 m in 1 minute. Find the minimum horsepower of the engine to be used.

Answer 1

Given:
Mass of the metal, $m=2000\mathrm{kg}$
Distance, s = 12 m
Time taken, t = 1 minute = 60 s
Force applied by the engine to lift the metal,
F = mg

$$\begin{gathered} \mathrm{So},\mathrm{work}\mathrm{done}\mathrm{by}\mathrm{the}\mathrm{engine}, \\ W=F\times s\times \cos \mathrm{\theta }=mgs\times \cos 0°[\mathrm{\theta }=0°\mathrm{for}\mathrm{minimum}\mathrm{force}] \\ =2000\times 10\times 12 \\ =240000\mathrm{J} \\ \mathrm{So},\mathrm{power}\mathrm{exerted}\mathrm{by}\mathrm{the}\mathrm{engine}, \\ P\mathit{=}\frac{W}{t} \\ =\frac{240000}{60}=4000\mathrm{watt} \\ \mathrm{Power}\mathrm{in}\mathrm{hp}, \\ P=\frac{4000}{746}=5.3\mathrm{hp} \end{gathered}$$